Related papers: A class of iterative methods for solving nonlinear…
In this work, we consider smooth unconstrained optimization problems and we deal with the class of gradient methods with momentum, i.e., descent algorithms where the search direction is defined as a linear combination of the current…
In this paper, we analyze the convergence %semi-convergence properties of projected non-stationary block iterative methods (P-BIM) aiming to find a constrained solution to large linear, usually both noisy and ill-conditioned, systems of…
Motivated by emerging applications in machine learning, we consider an optimization problem in a general form where the gradient of the objective function is available through a biased stochastic oracle. We assume a bias-control parameter…
We consider solving a probably ill-conditioned linear operator equation, where the operator is not modeled by physical laws but is specified via training pairs (consisting of images and data) of the input-output relation of the operator. We…
The subgradient method is a classical and foundational approach in non-smooth convex optimization; its simplicity, robustness, and role as a conceptual and algorithmic starting point have made it the backbone of many significant…
In this paper, we consider gradient methods for minimizing smooth convex functions, which employ the information obtained at the previous iterations in order to accelerate the convergence towards the optimal solution. This information is…
Many inverse problems are concerned with the estimation of non-negative parameter functions. In this paper, in order to obtain non-negative stable approximate solutions to ill-posed linear operator equations in a Hilbert space setting, we…
Quasidiagonal operators on a Hilbert space are a large and important class (containing all self-adjoint operators for instance). They are also perfectly suited for study via the finite section method (a particular Galerkin method). Indeed,…
Iterative algorithms are fundamental tools for approximating fixed-points of nonexpansive operators in real Hilbert spaces. Among them, Krasnosel'ski\u{\i}--Mann iteration and Halpern iteration are two widely used schemes. In this work, we…
In many applications, we need algorithms which can align partially overlapping point sets and are invariant to the corresponding transformations. In this work, a method possessing such properties is realized by minimizing the objective of…
This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal…
Considering the question: how non-linear may a non-linear operator be in order to extend the linear regularization theory, we introduce the class of dilinear mappings, which covers linear, bilinear, and quadratic operators between Banach…
In this paper we propose a variant of the random coordinate descent method for solving linearly constrained convex optimization problems with composite objective functions. If the smooth part of the objective function has Lipschitz…
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…
This paper uses the resolvent operator technique to investigate second-order non-autonomous neutral integrodifferential equations with impulsive conditions in a Banach space. We study the existence of a mild solution and the system's…
We consider a class of Riemannian optimization problems where the objective is the sum of a smooth function and a nonsmooth function, considered in the ambient space. This class of problems finds important applications in machine learning…
These lecture notes for a graduate class present the regularization theory for linear and nonlinear ill-posed operator equations in Hilbert spaces. Covered are the general framework of regularization methods and their analysis via spectral…
For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple…
In this paper we the formulation of inverse problems as constrained minimization problems and their iterative solution by gradient or Newton type. We carry out a convergence analysis in the sense of regularization methods and discuss…
In this paper, we propose some accelerated methods for solving optimization problems under the condition of relatively smooth and relatively Lipschitz continuous functions with an inexact oracle. We consider the problem of minimizing the…